On the mass-coupling relation of multi-scale quantum integrable models

TL;DR

This paper derives an exact mass-coupling relation for a two-scale quantum integrable model using conformal field theory reformulation, form factor perturbation theory, and numerical validation, providing a comprehensive analytical and numerical analysis.

Contribution

It introduces a novel approach to determine the mass-coupling relation in multi-scale quantum integrable models through reformulation and form factor techniques, with exact solutions and numerical confirmation.

Findings

Derived differential equations for the mass-coupling relation.

Solved the equations using hypergeometric functions.

Confirmed results with thermodynamic Bethe Ansatz data.

Abstract

We determine exactly the mass-coupling relation for the simplest multi-scale quantum integrable model, the homogenous sine-Gordon model with two independent mass-scales. We first reformulate its perturbed coset CFT description in terms of the perturbation of a projected product of minimal models. This representation enables us to identify conserved tensor currents on the UV side. These UV operators are then mapped via form factor perturbation theory to operators on the IR side, which are characterized by their form factors. The relation between the UV and IR operators is given in terms of the sought-for mass-coupling relation. By generalizing the $\Theta$ sum rule Ward identity we are able to derive differential equations for the mass-coupling relation, which we solve in terms of hypergeometric functions. We check these results against the data obtained by numerically solving the thermodynamic Bethe Ansatz equations, and find a complete agreement.